《高等數(shù)學(xué)》課程教學(xué)大綱

《高等數(shù)學(xué)》課程教學(xué)大綱課程名稱：高等數(shù)學(xué)(B)1課程類別（必修/選修）：必修課程英文名稱：AdvancedMathematics（B）1總學(xué)時(shí)/周學(xué)時(shí)/學(xué)分：48/3/3其中實(shí)驗(yàn)學(xué)時(shí)：無(wú)先修課程：高中數(shù)學(xué)授課時(shí)間：星期三5-7節(jié)授課地點(diǎn)：實(shí)314授課對(duì)象：2018級(jí)經(jīng)濟(jì)與金融專業(yè)答疑時(shí)間、地點(diǎn)與方式：星期三3-4節(jié),實(shí)202課程考核方式：作業(yè)（V）期中考（V）期末考（V）出勤（V）使用教材：JamesStewart,Calculus,7thEdition.教學(xué)參考資料：FinneyandThomas,Calculus,2ndEdition.課程簡(jiǎn)介：高等數(shù)學(xué)是高等學(xué)校各專業(yè)的一門重要基礎(chǔ)課程,它是工程數(shù)學(xué),統(tǒng)計(jì)機(jī)率,微分幾何等學(xué)科之基礎(chǔ),應(yīng)用層面也非常廣泛,主要有工程科學(xué)、自然科學(xué)?社會(huì)科學(xué)、經(jīng)濟(jì)學(xué)、醫(yī)學(xué)等各個(gè)領(lǐng)域?高等數(shù)學(xué)課程的學(xué)習(xí),不僅為學(xué)生后継專專業(yè)課的學(xué)習(xí)打下必要的數(shù)學(xué)基礎(chǔ),而且還能促進(jìn)學(xué)生的抽象思維和提高學(xué)生的推理能力,更能進(jìn)一步地應(yīng)用在自己專業(yè)領(lǐng)域上及生活實(shí)例上。課程教學(xué)目標(biāo)1.能理解極限的定義及如何做計(jì)算,分析連續(xù)的定義及其運(yùn)用特性,探討水平和垂直漸近綫,綜合所有基礎(chǔ)觀念來(lái)定義微分之概念。2.具有微分之概念,適當(dāng)?shù)剡\(yùn)用在多項(xiàng)式,指數(shù)函數(shù),三角函數(shù),對(duì)數(shù)函數(shù)和三角函數(shù)之微分；分析乘積,商數(shù)和連鎖法則；綜合所有法則及對(duì)一些函數(shù)求導(dǎo)數(shù)進(jìn)而計(jì)算其隱函數(shù)之微分。3.能理解函數(shù)之最大,最小,極大,極小和臨界點(diǎn)之定義,運(yùn)用羅爾斯及中間值定理,和不定式及羅畢達(dá)法則去分析函數(shù)之特性進(jìn)而描繪其圖形；具備牛頓法之概念進(jìn)而求解方程式；正確地計(jì)算函數(shù)之反導(dǎo)數(shù)。本課程與學(xué)生核心能力培養(yǎng)之間的關(guān)聯(lián)(授課對(duì)象為理工科專業(yè)學(xué)生的課程填寫此欄）：V核心能力1.應(yīng)用數(shù)學(xué)、基礎(chǔ)科學(xué)和機(jī)械設(shè)計(jì)制造及其自動(dòng)化專業(yè)知識(shí)的能力?！鹾诵哪芰?.設(shè)計(jì)與執(zhí)行實(shí)驗(yàn),以及分析與解釋數(shù)據(jù)的能力。V核心能力3.機(jī)械工程領(lǐng)域所需技能、技術(shù)以及使用軟硬件工具的能力?！鹾诵哪芰?.機(jī)械工程系統(tǒng)、零部件或工藝流程的設(shè)計(jì)能力?！鹾诵哪芰?.項(xiàng)目管理、有效溝通協(xié)調(diào)、團(tuán)隊(duì)合作及創(chuàng)新能力。V核心能力6.發(fā)掘、分析與解決復(fù)雜機(jī)械工程問(wèn)題的能力。V核心能力7．認(rèn)識(shí)科技發(fā)展現(xiàn)狀與趨勢(shì),了解工程技術(shù)對(duì)環(huán)境、社會(huì)及全球的影珦,并培養(yǎng)持續(xù)學(xué)習(xí)的習(xí)慣與能力。V核心能力8．理解職業(yè)道德、專業(yè)倫理與認(rèn)知社會(huì)責(zé)任的能力。理論教學(xué)進(jìn)程表周次教學(xué)主題教學(xué)時(shí)長(zhǎng)教學(xué)的重點(diǎn)與難點(diǎn)教學(xué)方式作業(yè)安排41.5ExponentialFunctions1.6InverseFunctionsandLogarithms3KeyPoint:Learnsomeexponential,inversefunctionsandlogarithms..Difficulty:Becarefultocomputeexponential,inversefunctionsandlogarithms.teachExercises1.5&1.652.1TheTangentandVelocityProblems2.2TheLimitofaFunction3KeyPoint:Learnhowtodrawthetangentanduseittodefinethelimitofafunction.Difficulty:Becarefultocomputethelimitofafunction.teachExercises2.1&2.262.3CalculatingLimitsUsingtheLimitLaws.2.4ThePreciseDefinitionofaLimit.3KeyPoint:Learnhowtocomputethelimit.Difficulty:Usingtheprecisedefinitiontoprovethelimit.teachExercises2.3&2.472.5Continuity3KeyPoint:Learnthedefinitionofthecontinuityandsomeproperties.Difficulty:Showthecontinuousfunctionontheinterval.teachExercises2.582.6LimitsatInfinity;HorizontalAsymptotes.3KeyPoint:Learnthedefinitionofhorizontalasymptotes.Difficulty:Usingtheprecisedefinitiontoprovehorizontalasymptotes.teachExercises2.692.7DerivativesandRatesofChange.2.8TheDerivativeasaFunction.3KeyPoint:Learnthedefinitionofhorizontalasymptotesandderivatives.Difficulty:Usingtheprecisedefinitiontoprovehorizontalasymptotesandbecarefultocomputethehigherderivatives.teachAssignment1Exercises2.7&2.8103.1DerivativesofPolynomialsandExponentialFunctions.3.2TheProductandQuotientRules.3KeyPoint:Learnhowtocomputederivativesofpolynomialsandexponentialfunctions,thengetsomerulesofproductandquotient.Difficulty:Usingtheprecisedefinitiontoprovehorizontalasymptotesandbecarefultocomputethehigherderivatives.teachExercises3.1&3.211Mid-TermTest3Mid-TermTestNoneNone123.3DerivativesofTrigonometricFunctions.3.4TheChainRule3KeyPoint:LearnhowtocomputederivativesoftrigonometricfunctionsandChainRule.Difficulty:Becarefultocomputethederivativesoftrigonometricfunctions.teachExercises3.3&3.4133.5ImplicitDifferentiation3KeyPoint:Learnimplicitdifferentiationandhowtocomputederivativesofinversetrigonometricfunctions.Difficulty:Becarefultocomputederivativesofinversetrigonometricfunctions.teachExercises3.5143.6DerivativesofLogarithmicFunctions.3.11HyperbolicFunctions3KeyPoint:Learnsomederivativesoflogarithmicandhyperbolicfunctions.Difficulty:Becarefultocomputederivativesoflogarithmicandhyperbolicfunctions.teachExercises3.6&3.11154.1MaximumandMinimumValues.3KeyPoint:Learnabsolutemaximumandminimum;localmaximumandminimum;criticalnumbers.Difficulty:Howtofindabsoluteandlocalvaluesoffunctions.teachAssignment2Exercises4.1164.2TheMeanValueTheorem4.3HowDerivativesAffecttheShapeofaGraph3KeyPoint:LearnRolle’stheoremandthemeanvaluetheorem,thendrawthegraphsofsomefunctions.Difficulty:Becarefultosketchthegraphaccordingtothefirstandsecondderivativetests.teachExercises4.2&4.3174.4IndeterminateFormsandL’Hospital’sRule.4.5SummaryofCurveSketching.3KeyPoint:LearnindeterminateformanduseL’Hospitalruletosolvethem,thenlearnhowtodrawcurvesoffunctions.Difficulty:BecarefultocomputethelimitsapplyingL’Hospital’sruleanddrawthecurves.teachExercises4.4&4.5184.6GraphingwithCalculusandCalculators.4.8Newton’sMethod3KeyPoint:Learnsomepropertiesandsketchthecurves,thenlearnNewton’smethod.Difficulty:BecarefultosketchcurvesandsolveequationsusingNewton’smethod.teachExercises4.6&4.8194.9Antiderivatives3KeyPoint:Learnsomeantiderivativesoffunctions.Difficulty:Becarefultocomputeantiderivativesoffunctions.teachExercises4.9合計(jì)：48成績(jī)?cè)u(píng)定方法及標(biāo)準(zhǔn)考核形式評(píng)價(jià)標(biāo)準(zhǔn)權(quán)重Mid-TermTestScoresaccordingtostandardanswers30%FinalTestScoresaccordingtostandardanswers40%AssignmentHandinassignmentsontimeandnoplagiarism.20%AttendanceNoarrivelate,noleaveearly,noabsence.10%大綱編寫時(shí)間：2018.9.13系（部）審查意見：我系（專業(yè)）已對(duì)本課程教學(xué)